The Swans reached this stage of the competition for the first time since 1964 after brushing aside Sheffield Wednesday at the Liberty Stadium.
And, although, Swansea have only won twice in all their 18 previous meetings with the Lillywhites, the Anglo-Nigerian is hoping they can upset their visitors.
“There is a chance to do something special in the cup this season but Tottenham are a fantastic team,” Abraham told club website.
“We just have to go out and produce our A game – nothing less than that will do.
“Tottenham won’t come and sit back. They will come all guns blazing and we have to do the same. We have to believe we can do it.
“Tottenham are a top-class team, but we earned a decent point against them at Wembley earlier this season.
“We just have to stick together on Saturday. They are coming to our ground, so we need to make it difficult for them to get a win.”
Though hampered by injury and loss of form, the 20-year-old has scored seven goals, including two in the FA Cup this season and will be looking to add to his haul on Saturday.